Question

How do you graph `5x-2y=10`?

Answer 1

See the explanation.

Explanation:

Graph:

`5x-2y=10`

This equation is in standard form for a linear equation. You only need two points to graph a straight line. The standard form makes it easy to find the x- and y-intercepts, which can be graphed.

`5x-2y=10`

X-intercept: value of `x` when `y=0`.

Substitute `0` fro `y` and solve for `x`.

`5x-2(0)=10`

`5x=10`

Divide both sides by `5`.

`x=10/5`

`x=2`

The x-intercept is `(2,0)`.

Y-intercept: value of `y` when `x=0`

Substitute `0` for `x` and solve for `y`.

`5(0)-2y=10`

`-2y=10`

Divide both sides by `-2`.

`y=10/-2`

`y=-5`

The y-intercept is `(0,-5)`

Plot the x- and y-intercepts and draw a straight line through the points.

graph{5x-2y=10 [-16.23, 15.8, -10.26, 5.76]}

Answer 2

Find the `x and y`- intercepts and draw a line through them.

Explanation:

If you are given the equation of a straight line in standard form
`(ax+by =c)`, then you can find the `x and y`-intercepts.

To find the `x`-intercept, make `color(red)(y=0)`

`5x-2color(red)(y) = 10" "rarr5x-2color(red)((0)) = 10" "` Solve for `x`
`5x = 10`

`x = 2" "larr` this is the `x`-intercept

To find the `y`-intercept, make `color(blue)(x=0)`

`5color(blue)(x)-2y = 10" "rarr5color(blue)((0))-2y = 10" "` Solve for `y`
`-2y = 10`

`y=-5" "larr` this is the `y`-intercept

Now you can plot the two intercepts on a grid and draw a line passing through both of them. graph{5x-2y = 10 [-6.06, 13.94, -8.06, 1.94]}